On the Nonspecular Reflection of Sound from Planes with Absorbent Bosses

The nonspecular reflection of plane waves of sound from certain surfaces composed of absorbent bosses (semicylinders or hemispheres of arbitrary impedance) on an infinite plane of ∞ or 0 impedance is considered. Exact solutions are obtained for the problem of the single boss and then extended, subject to the single‐scattering hypothesis, to obtain far field solutions for certain planar distributions of bosses of radii small compared with the wavelength. The results are compared with those obtained previously for non‐absorbent bosses, and it is shown that the effects of the finite impedance are most pronounced in the simple source terms of the scattered components and may lead to either a decrease or an increase in the radiation reflected at the specular angle. Another effect of the finite impedance (for the small finite distributions) is to shift the critical value of the angle of incidence for which the reflection at the specular angle consists only of the specular component—below this value the reflection at the specular angle being a minimum and above it a maximum. For the infinite uniform random distributions it is found that the effect of the bosses is essentially but to change the impedance of the plane—these effective impedances being functions of the angle of incidence and the parameters and distribution of the bosses. The effect of the finite impedance of the bosses is most pronounced for these distributions yielding terms much lager than those previously retained for the nonabsorbent bosses. The results for the analogous distributions of cylinders and spheres are also given.